Theorems · Theorem · global analysis

MDifferentiableWithinAt.inv

∀ {𝕜 : Type u_1} [inst : NontriviallyNormedField 𝕜] {E : Type u_2} [inst_1 : NormedAddCommGroup E]
  [inst_2 : NormedSpace 𝕜 E] {H : Type u_3} [inst_3 : TopologicalSpace H] {I : ModelWithCorners 𝕜 E H} {M : Type u_4}
  [inst_4 : TopologicalSpace M] [inst_5 : ChartedSpace H M] {s : Set M} {z : M} {F' : Type u_21}
  [inst_6 : NormedDivisionRing F'] [inst_7 : NormedAlgebra 𝕜 F'] {p : M → F'},
  MDiffAt[s] p z → p z ≠ 0 → MDiffAt[s] p⁻¹ z

Defined in

Mathlib.Geometry.Manifold.MFDeriv.SpecificFunctions

Cited by

3 results in Mathlib

Foundations

Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NontriviallyNormedFieldNormedAddCommGroupNormedSpaceTopologicalSpaceTopologicalSpaceChartedSpaceNormedDivisionRingNormedAlgebra